Pólya’s Proof of the Weighted Arithmetic-Geometric Mean Inequality

Manuel Eberl
Archive of Formal Proofs 2022.

 pdf AFP entry

Abstract

This article provides a formalisation of the Weighted Arithmetic–Geometric Mean Inequality. As a corollary, the regular arithmetic–geometric mean inequality follows. I follow Pólya’s elegant proof, which uses the inequality exp(x) ≥ 1 + x as a starting point. Pólya claims that this proof came to him in a dream, and that it was “the best mathematics he had ever dreamt.”

BibTex

@article{Weighted_Arithmetic_Geometric_Mean-AFP,
author = {Manuel Eberl},
title = {Pólya’s Proof of the Weighted Arithmetic–Geometric Mean Inequality},
journal = {Archive of Formal Proofs},
month = {July},
year = {2022},
note = {\url{https://isa-afp.org/entries/Weighted_Arithmetic_Geometric_Mean.html},
Formal proof development},
ISSN = {2150-914x},
}